The triangular panel $ABC$ forms part of a pavilion. Side $AB$ is extended beyond $B$ to $D$

Question

The triangular panel $ABC$ forms part of a pavilion. Side $AB$ is extended beyond $B$ to $D$. The angles are shown below. By forming an equation in $x$, find $x$. [2] A window in the pavilion is a convex octagon, a polygon with eight sides. [4] Find the sum of its interior angles. [1] Five exterior angles of the window are each $40^\circ$. The other three are $$ (y+10)^\circ,\qquad (y+20)^\circ,\qquad (2y+10)^\circ. $$ Find the largest interior angle of the window. Show your working. [3]

Accepted Answer

(a) $x=20$. (b)(i) $1080^\circ$. (b)(ii) $140^\circ$.

Polygons - Triangle Angle Sum and Exterior Angles

Polygons - Triangle Angle Sum and Exterior Angles

Solution:

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